- Curve-shortening Flow and Surfaces
- Project Year:
2018
- REU Student (s):
Scott Harman | Rutgers University-New Brunswick NJ
- Student 1 Institution:
Rutgers University-New Brunswick
- Project Mentor:
Christopher Woodward
- Project Mentor Area:
Mathematics
- Project Abstract:
The curve-shortening flow is a process that modifies curves in the plane according to a certain partial differential equation. With certain starting conditions, the flow will shorten the perimeter and cause the curve to collapse to a circle, and then to a point, in finite time. The flow in the plane has been extensively studied, but we extend the notion of the flow to surfaces. We investigate how the evolution equation must be adapted so that the flow is well-defined, and then analyze certain surfaces and families of curves that provide a solution on those surfaces. We then pose certain open questions that will be studied further.
